1) Automatically go to the next video or quiz upon reaching the end of the current video.

2) Selects 720p video quality by default and changes page layout to accommodate this size. Quizes and programming editor needs further work (as I update the code on userscript all installed scripts will be automatically updated)

Tested on Chrome. Should also work on FF and Opera.
This script can can be installed as an Chrome extension or as a tampermonkey script.

Is there (or maybe could there be) a possibility to watch videos in a faster pace like it is implemented in db-class?

It's often convenient and practical to skim through the material we are (for instance) already familiar with and I guess that many users would find such an option useful especially when checking their answers to the quizzes.

Enabling HTML5 on Youtube only offers 1.5x and 2x speedup by default. There's a property 'playbackRate', though, which you can set to custom values (document.getElementsByClassName('video-stream')[0].playbackRate=##, found on Udacity forum)

@rhasarub would it be possible to have a userscript that opts in HTML5 trial and add options to speed up by 10% like for Coursera videos ? I guess it should be possible? Haven't dabbled in Chrome extension coding